Homogenization estimates for hyperelastic composites and particle-reinforced rubbers

This Note is concerned with the development of variational estimates for the effective stored-energy function of hyperelastic composites undergoing finite deformations. It makes use of a suitable generalization of the "second-order procedure" of Ponte Castaneda, the key idea being the introduction of an optimally chosen "linear thermoelastic comparison composite", which can then be used to convert available homogenization estimates for linear systems directly into new estimates for hyperelastic composites. The resulting estimates are known to be exact to second order in the contrast. An application is given for particle-reinforced rubbers. (C) 1999 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.